Language models, potentially augmented with tool usage such as retrieval are becoming the go-to means of answering questions. Understanding and answering questions in real-world settings often requires retrieving information from different sources, processing and aggregating data to extract insights, and presenting complex findings in form of structured artifacts such as novel tables, charts, or infographics. In this paper, we introduce TANQ, the first open domain question answering dataset where the answers require building tables from information across multiple sources. We release the full source attribution for every cell in the resulting table and benchmark state-of-the-art language models in open, oracle, and closed book setups. Our best-performing baseline, GPT4 reaches an overall F1 score of 29.1, lagging behind human performance by 19.7 points. We analyse baselines' performance across different dataset attributes such as different skills required for this task, including multi-hop reasoning, math operations, and unit conversions. We further discuss common failures in model-generated answers, suggesting that TANQ is a complex task with many challenges ahead.